Ranks of elliptic curves over Z_p^2-extensions

Antonio Lei; Florian Sprung

Ranks of elliptic curves over Z_p^2-extensions

Number Theory 2018-09-27 v1

Authors: Antonio Lei , Florian Sprung

Abstract

Let $E$ be an elliptic curve with good reduction at a fixed odd prime $p$ and $K$ an imaginary quadratic field where $p$ splits. We give a growth estimate for the Mordell-Weil rank of $E$ over finite extensions inside the $\mathbb{Z}_p^2$ -extension of $K$ .

Keywords

elliptic curves mordell-weil rank z_p^2-extensions imaginary quadratic fields good reduction growth estimate

Cite

@article{arxiv.1809.10127,
  title  = {Ranks of elliptic curves over Z_p^2-extensions},
  author = {Antonio Lei and Florian Sprung},
  journal= {arXiv preprint arXiv:1809.10127},
  year   = {2018}
}

Comments

15 pages, plus references

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